On the page forms of main verbs chart, at the bottom:- to be has 9 forms: to be, be, was, were, been, being, am, is, are.

This is contested by my tutor with the following comments

You can certainly add to in front to make an infinitive verb, but infinitive verbs with or without "to" are not (art of Stative verbs) and are only shown to esl learners who are beginners as they then tend to use them everywhere.

I am reminded that stative verbs are:- 1: is, 2: are 3:was 4:were 5:am, 6:be 7:being 8:been. Thus making a total of 8.

For what it's worth, I concur with your tutor: it is quite meaningless to distinguish between an infinitive with, and an infinitive without, 'to' as two distinct forms of the same verb, when they can never be different!